
'''simple docstring'''






def 		A_							(						_lowerCAmelCase :     List[Any]					,						_lowerCAmelCase :     Any				):



      """simple docstring"""




      return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2







def 		A_							(						_lowerCAmelCase :     Any					,						_lowerCAmelCase :     str=0				):



      """simple docstring"""




      return sorted(_lowerCAmelCase					,						key=lambda _lowerCAmelCase				: x[column]				)







def 		A_							(						_lowerCAmelCase :     Optional[int]					,						_lowerCAmelCase :     Optional[int]					,						_lowerCAmelCase :     Tuple=float("inf"				)				):



      """simple docstring"""




      for i in range(points_counts - 1				):
            for j in range(i + 1					,						_lowerCAmelCase				):
                  _lowerCamelCase					: Optional[Any]		    = euclidean_distance_sqr(points[i]					,						points[j]				)
                  if current_dis < min_dis:
                        _lowerCamelCase					: Optional[int]		    = current_dis
      return min_dis







def 		A_							(						_lowerCAmelCase :     List[str]					,						_lowerCAmelCase :     Any					,						_lowerCAmelCase :     str=float("inf"				)				):



      """simple docstring"""




      for i in range(min(6					,						points_counts - 1				)					,						_lowerCAmelCase				):
            for j in range(max(0					,						i - 6				)					,						_lowerCAmelCase				):
                  _lowerCamelCase					: Any		    = euclidean_distance_sqr(points[i]					,						points[j]				)
                  if current_dis < min_dis:
                        _lowerCamelCase					: Optional[int]		    = current_dis
      return min_dis







def 		A_							(						_lowerCAmelCase :     Tuple					,						_lowerCAmelCase :     Tuple					,						_lowerCAmelCase :     str				):



      """simple docstring"""




      if points_counts <= 3:
            return dis_between_closest_pair(_lowerCAmelCase					,						_lowerCAmelCase				)

      # recursion
      _lowerCamelCase					: int		    = points_counts // 2
      _lowerCamelCase					: Dict		    = closest_pair_of_points_sqr(
          _lowerCAmelCase					,						points_sorted_on_y[:mid]					,						_lowerCAmelCase				)
      _lowerCamelCase					: Optional[Any]		    = closest_pair_of_points_sqr(
          _lowerCAmelCase					,						points_sorted_on_y[mid:]					,						points_counts - mid				)
      _lowerCamelCase					: Tuple		    = min(_lowerCAmelCase					,						_lowerCAmelCase				)
      _lowerCamelCase					: Optional[Any]		    = []
      for point in points_sorted_on_x:
            if abs(point[0] - points_sorted_on_x[mid][0]				) < closest_pair_dis:
                  cross_strip.append(_lowerCAmelCase				)

      _lowerCamelCase					: Union[str, Any]		    = dis_between_closest_in_strip(
          _lowerCAmelCase					,						len(_lowerCAmelCase				)					,						_lowerCAmelCase				)
      return min(_lowerCAmelCase					,						_lowerCAmelCase				)







def 		A_							(						_lowerCAmelCase :     Tuple					,						_lowerCAmelCase :     List[str]				):



      """simple docstring"""




      _lowerCamelCase					: Tuple		    = column_based_sort(_lowerCAmelCase					,						column=0				)
      _lowerCamelCase					: int		    = column_based_sort(_lowerCAmelCase					,						column=1				)
      return (
          closest_pair_of_points_sqr(
              _lowerCAmelCase					,						_lowerCAmelCase					,						_lowerCAmelCase				)
      ) ** 0.5


if __name__ == "__main__":
 UpperCAmelCase_							: Tuple =							[(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
 print('Distance:', closest_pair_of_points(points, len(points)))
from __future__ import annotations

from collections import Counter
from random import random




class 					_UpperCAmelCase			:



 '''simple docstring'''




 def __init__(		self				:   List[str])						->	Any:


   """simple docstring"""







   _UpperCamelCase           =    {}







 def 		__UpperCAmelCase				(		self				:   Optional[Any]							, lowercase_				:   str)						->	None:


   """simple docstring"""







   _UpperCamelCase           =    {}







 def 		__UpperCAmelCase				(		self				:   List[str]							, lowercase_				:   str							, lowercase_				:   str							, lowercase_				:   float)						->	None:


   """simple docstring"""







   if nodea not in self.connections:
     self.add_node(lowercase_)
   if nodea not in self.connections:
     self.add_node(lowercase_)
   _UpperCamelCase           =    probability







 def 		__UpperCAmelCase				(		self				:   Any)						->	list[str]:


   """simple docstring"""







   return list(self.connections)







 def 		__UpperCAmelCase				(		self				:   Tuple							, lowercase_				:   str)						->	str:


   """simple docstring"""







   _UpperCamelCase           =    0
   _UpperCamelCase           =    random()

   for dest in self.connections[node]:
     current_probability += self.connections[node][dest]
     if current_probability > random_value:
       return dest
   return ""


def 				lowerCAmelCase__       (			a__    ,     a__    ,     a__ )      ->dict[str, int]:




  '''simple docstring'''

  _UpperCamelCase           =    MarkovChainGraphUndirectedUnweighted()

  for nodea, nodea, probability in transitions:
    graph.add_transition_probability(a__    ,     a__    ,     a__ )

  _UpperCamelCase           =    Counter(graph.get_nodes() )
  _UpperCamelCase           =    start

  for _ in range(a__ ):
    _UpperCamelCase           =    graph.transition(a__ )
    visited[node] += 1

  return visited


if __name__ == "__main__":
   import doctest

   doctest.testmod()




